Problem: Boolean Expression Compressor

You are asked to build a compressor for Boolean expressions that transforms expressions to the shortest form keeping their meaning.

The grammar of the Boolean expressions has terminals `0` `1` `a` `b` `c` `d` `-` `^` `*` `(` `)`, start symbol <E> and the following production rule:

> <E>  ::=  `0`  |  `1`  |  `a`  |  `b`  |  `c`  |  `d`  |  `-`<E>  |  `(`<E>`^`<E>`)`  |  `(`<E>`*`<E>`)`

Letters `a`, `b`, `c` and `d` represent Boolean variables that have values of either `0` or `1`. Operators are evaluated as shown in the Table below. In other words, `-` means negation (NOT), `^` means exclusive disjunction (XOR), and `*` means logical conjunction (AND).

Table: Evaluations of operators
<image>

Write a program that calculates the length of the shortest expression that evaluates equal to the given expression with whatever values of the four variables.

For example, `0`, that is the first expression in the sample input, cannot be shortened further. Therefore the shortest length for this expression is 1.

For another example, `(a*(1*b))`, the second in the sample input, always evaluates equal to `(a*b)` and `(b*a)`, which are the shortest. The output for this expression, thus, should be `5`.

Input

The input consists of multiple datasets. A dataset consists of one line, containing an expression conforming to the grammar described above. The length of the expression is less than or equal to 16 characters.

The end of the input is indicated by a line containing one `.` (period). The number of datasets in the input is at most 200.

Output

For each dataset, output a single line containing an integer which is the length of the shortest expression that has the same value as the given expression for all combinations of values in the variables.

Sample Input


0
(a*(1*b))
(1^a)
(-(-a*-b)*a)
(a^(b^(c^d)))
.


Output for the Sample Input


1
5
2
1
13






Example

Input

0
(a*(1*b))
(1^a)
(-(-a*-b)*a)
(a^(b^(c^d)))
.


Output

1
5
2
1
13

Solution (in CPP):

Solution:
#define  _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES

#pragma comment (linker, "/STACK:526000000")

#include "bits/stdc++.h"

using namespace std;
typedef string::const_iterator State;
#define eps 1e-5L
#define MAX_MOD 1000000007LL
#define GYAKU 500000004LL
#define MOD 998244353LL
#define pb push_back
#define mp make_pair
typedef long long ll;
#define REP(a,b) for(long long (a) = 0;(a) < (b);++(a))
#define ALL(x) (x).begin(),(x).end()

// geometry library

typedef complex<long double> Point;
typedef pair<complex<long double>, complex<long double>> Line;

typedef struct Circle {
    complex<long double> center;
    long double r;
}Circle;

long double dot(Point a, Point b) {
    return (a.real() * b.real() + a.imag() * b.imag());
}
long double cross(Point a, Point b) {
    return (a.real() * b.imag() - a.imag() * b.real());
}

long double Dist_Line_Point(Line a, Point b) {
    if (dot(a.second - a.first, b - a.first) < eps) return abs(b - a.first);
    if (dot(a.first - a.second, b - a.second) < eps) return abs(b - a.second);
    return abs(cross(a.second - a.first, b - a.first)) / abs(a.second - a.first);
}

int is_intersected_ls(Line a, Line b) {
    return (cross(a.second - a.first, b.first - a.first) * cross(a.second - a.first, b.second - a.first) < eps) &&
        (cross(b.second - b.first, a.first - b.first) * cross(b.second - b.first, a.second - b.first) < eps);
}

Point intersection_l(Line a, Line b) {
    Point da = a.second - a.first;
    Point db = b.second - b.first;
    return a.first + da * cross(db, b.first - a.first) / cross(db, da);
}

long double Dist_Line_Line(Line a, Line b) {
    if (is_intersected_ls(a, b) == 1) {
        return 0;
    }
    return min({ Dist_Line_Point(a,b.first), Dist_Line_Point(a,b.second),Dist_Line_Point(b,a.first),Dist_Line_Point(b,a.second) });
}

pair<Point, Point> intersection_Circle_Circle(Circle a, Circle b) {
    long double dist = abs(a.center - b.center);
    assert(dist <= eps + a.r + b.r);
    assert(dist + eps >= abs(a.r - b.r));
    Point target = b.center - a.center;
    long double pointer = target.real() * target.real() + target.imag() * target.imag();
    long double aa = pointer + a.r * a.r - b.r * b.r;
    aa /= 2.0L;
    Point l{ (aa * target.real() + target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,
            (aa * target.imag() - target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };
    Point r{ (aa * target.real() - target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,
        (aa * target.imag() + target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };
    r = r + a.center;
    l = l + a.center;
    return mp(l, r);
}

//end of geometry

template<typename A>
A pows(A val, ll b) {
    assert(b >= 1);
    A ans = val;
    b--;
    while (b) {
        if (b % 2) {
            ans *= val;
        }
        val *= val;
        b /= 2LL;
    }
    return ans;
}

template<typename A>
class Compressor {
public:
    bool is_zipped = false;
    map<A, ll> zipper;
    map<ll, A> unzipper;
    queue<A> fetcher;
    Compressor() {
        is_zipped = false;
        zipper.clear();
        unzipper.clear();
    }
    void add(A now) {
        assert(is_zipped == false);
        zipper[now] = 1;
        fetcher.push(now);
    }
    void exec() {
        assert(is_zipped == false);
        int cnt = 0;
        for (auto i = zipper.begin(); i != zipper.end(); ++i) {
            i->second = cnt;
            unzipper[cnt] = i->first;
            cnt++;
        }
        is_zipped = true;
    }
    ll fetch() {
        assert(is_zipped == true);
        A hoge = fetcher.front();
        fetcher.pop();
        return zipper[hoge];
    }
    ll zip(A now) {
        assert(is_zipped == true);
        assert(zipper.find(now) != zipper.end());
        return zipper[now];
    }
    A unzip(ll a) {
        assert(is_zipped == true);
        assert(a < unzipper.size());
        return unzipper[a];
    }
    ll next(A now) {
        auto x = zipper.upper_bound(now);
        if (x == zipper.end()) return zipper.size();
        return (ll)((*x).second);
    }
    ll back(A now) {
        auto x = zipper.lower_bound(now);
        if (x == zipper.begin()) return -1;
        x--;
        return (ll)((*x).second);
    }
};

template<typename A>
class Matrix {
public:
    vector<vector<A>> data;
    Matrix(vector<vector<A>> a) :data(a) {

    }
    Matrix operator + (const Matrix obj) {
        vector<vector<A>> ans;
        assert(obj.data.size() == this->data.size());
        assert(obj.data[0].size() == this->data[0].size());
        REP(i, obj.data.size()) {
            ans.push_back(vector<A>());
            REP(q, obj.data[i].size()) {
                A hoge = obj.data[i][q] + (this->data[i][q]);
                ans.back().push_back(hoge);
            }
        }
        return Matrix(ans);
    }
    Matrix operator - (const Matrix obj) {
        vector<vector<A>> ans;
        assert(obj.data.size() == this->data.size());
        assert(obj.data[0].size() == this->data[0].size());
        REP(i, obj.data.size()) {
            ans.push_back(vector<A>());
            REP(q, obj.data[i].size()) {
                A hoge = this->data[i][q] - obj.data[i][q];
                ans.back().push_back(hoge);
            }
        }
        return Matrix(ans);
    }
    Matrix operator * (const Matrix obj) {
        vector<vector<A>> ans;
        assert(obj.data.size() == this->data[0].size());
        REP(i, this -> data.size()) {
            ans.push_back(vector<A>());
            REP(q, obj.data[0].size()) {
                A hoge = (this->data[i][0]) * (obj.data[0][q]);
                for (int t = 1; t < obj.data[i].size(); ++t) {
                    hoge += this->data[i][t] * obj.data[t][q];
                }
                ans.back().push_back(hoge);
            }
        }
        return Matrix(ans);
    }
    Matrix& operator *= (const Matrix obj) {
        *this = (*this * obj);
        return *this;
    }
    Matrix& operator += (const Matrix obj) {
        *this = (*this + obj);
        return *this;
    }
    Matrix& operator -= (const Matrix obj) {
        *this = (*this - obj);
        return *this;
    }
};

class modint {
public:
    using u64 = std::uint_fast64_t;
    u64 value = 0;
    u64 mod;
    modint(ll a, ll b) : value(((a% b) + 2 * b) % b), mod(b) {

    }
    modint operator+(const modint rhs) const {
        return modint(*this) += rhs;
    }
    modint operator-(const modint rhs) const {
        return modint(*this) -= rhs;
    }
    modint operator*(const modint rhs) const {
        return modint(*this) *= rhs;
    }
    modint operator/(const modint rhs) const {
        return modint(*this) /= rhs;
    }
    modint& operator+=(const modint rhs) {
        assert(rhs.mod == mod);
        value += rhs.value;
        if (value >= mod) {
            value -= mod;
        }
        return *this;
    }
    modint& operator-=(const modint rhs) {
        assert(rhs.mod == mod);
        if (value < rhs.value) {
            value += mod;
        }
        value -= rhs.value;
        return *this;
    }
    modint& operator*=(const modint rhs) {
        assert(rhs.mod == mod);
        value = (value * rhs.value) % mod;
        return *this;
    }
    modint& operator/=(modint rhs) {
        assert(rhs.mod == mod);
        ll rem = mod - 2;
        while (rem) {
            if (rem % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            rem /= 2LL;
        }
        return *this;
    }
    bool operator <(modint rhs) const {
        return value < rhs.value;
    }
    friend ostream& operator<<(ostream& os, modint& p) {
        os << p.value;
        return (os);
    }
};

class Dice {
public:
    vector<ll> vertexs;
    //Up: 0,Left: 1,Center: 2,Right: 3,Adj: 4, Down: 5
    Dice(vector<ll> init) :vertexs(init) {

    }
    //Look from Center
    void RtoL() {
        for (int q = 1; q < 4; ++q) {
            swap(vertexs[q], vertexs[q + 1]);
        }
    }
    void LtoR() {
        for (int q = 3; q >= 1; --q) {
            swap(vertexs[q], vertexs[q + 1]);
        }
    }
    void UtoD() {
        swap(vertexs[5], vertexs[4]);
        swap(vertexs[2], vertexs[5]);
        swap(vertexs[0], vertexs[2]);
    }
    void DtoU() {
        swap(vertexs[0], vertexs[2]);
        swap(vertexs[2], vertexs[5]);
        swap(vertexs[5], vertexs[4]);
    }
    bool ReachAble(Dice now) {
        set<Dice> hoge;
        queue<Dice> next;
        next.push(now);
        hoge.insert(now);
        while (next.empty() == false) {
            Dice seeing = next.front();
            next.pop();
            if (seeing == *this) return true;
            seeing.RtoL();
            if (hoge.count(seeing) == 0) {
                hoge.insert(seeing);
                next.push(seeing);
            }
            seeing.LtoR();
            seeing.LtoR();
            if (hoge.count(seeing) == 0) {
                hoge.insert(seeing);
                next.push(seeing);
            }
            seeing.RtoL();
            seeing.UtoD();
            if (hoge.count(seeing) == 0) {
                hoge.insert(seeing);
                next.push(seeing);
            }
            seeing.DtoU();
            seeing.DtoU();
            if (hoge.count(seeing) == 0) {
                hoge.insert(seeing);
                next.push(seeing);
            }
        }
        return false;
    }
    bool operator ==(const Dice& a) {
        for (int q = 0; q < 6; ++q) {
            if (a.vertexs[q] != (*this).vertexs[q]) {
                return false;
            }
        }
        return true;
    }
    bool operator <(const Dice& a) const {
        return (*this).vertexs < a.vertexs;
    }
};

pair<Dice, Dice> TwoDimDice(int center, int up) {
    int target = 1;
    while (true) {
        if (center != target && 7 - center != target && up != target && 7 - up != target) {
            break;
        }
        target++;
    }
    return mp(Dice(vector<ll>{up, target, center, 7 - target, 7 - center, 7 - up}), Dice(vector<ll>{up, 7 - target, center, target, 7 - center, 7 - up}));
}

tuple<Dice, Dice, Dice, Dice> OneDimDice(int center) {
    int bo = min(center, 7 - center);
    pair<int, int> goa;
    if (bo == 1) {
        goa = mp(2, 3);
    }
    else if (bo == 2) {
        goa = mp(1, 3);
    }
    else if (bo == 3) {
        goa = mp(1, 2);
    }
    tuple<Dice, Dice, Dice, Dice> now = make_tuple(Dice(vector<ll>{goa.first, goa.second, center, 7 - goa.second, 7 - center, 7 - goa.first}),
        Dice(vector<ll>{goa.first, 7 - goa.second, center, goa.second, 7 - center, 7 - goa.first}),
        Dice(vector<ll>{7 - goa.first, goa.second, center, 7 - goa.second, 7 - center, goa.first}),
        Dice(vector<ll>{7 - goa.first, 7 - goa.second, center, goa.second, 7 - center, goa.first}));
    return now;
}

template<typename A, typename B>
class Dijkstra {
public:
    vector<vector<pair<int, A>>> vertexs;
    B Cost_Function;
    Dijkstra(int n, B cost) : Cost_Function(cost) {
        vertexs = vector<vector<pair<int, A>>>(n, vector<pair<int, A>>{});
    }
    ~Dijkstra() {
        vertexs.clear();
    }
    void add_edge(int a, int b, A c) {
        vertexs[a].push_back(mp(b, c));
    }
    vector<ll> build_result(int StartPoint) {
        vector<ll> dist(vertexs.size(), 2e18);
        dist[StartPoint] = 0;
        priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> next;
        next.push(make_pair(0, StartPoint));
        while (next.empty() == false) {
            pair<ll, int> now = next.top();
            next.pop();
            if (dist[now.second] != now.first) continue;
            for (auto x : vertexs[now.second]) {
                ll now_cost = now.first + Cost_Function(x.second);
                if (dist[x.first] > now_cost) {
                    dist[x.first] = now_cost;
                    next.push(mp(now_cost, x.first));
                }
            }
        }
        return dist;
    }
};

class Dinic {
public:
    struct edge {
        int to;
        int cap;
        int rev;
    };
    vector<vector<edge>> Graph;
    vector<int> level;
    vector<int> itr;
    Dinic(int n) {
        Graph = vector<vector<edge>>(n, vector<edge>());
    }
    void add_edge(int a, int b, int cap) {
        Graph[a].push_back(edge{ b, cap ,(int)Graph[b].size() });
        Graph[b].push_back(edge{ a,0,(int)Graph[a].size() - 1 });
    }
    void bfs(int s) {
        level = vector<int>(Graph.size(), -1);
        level[s] = 0;
        queue<int> next;
        next.push(s);
        while (next.empty() == false) {
            int now = next.front();
            next.pop();
            for (auto x : Graph[now]) {
                if (x.cap == 0) continue;
                if (level[x.to] == -1) {
                    level[x.to] = level[now] + 1;
                    next.push(x.to);
                }
            }
        }
    }
    int dfs(int now, int goal, int val) {
        if (goal == now) return val;
        for (int& i = itr[now]; i < (int)Graph[now].size(); ++i) {
            edge& target = Graph[now][i];
            if (target.cap > 0 && level[now] < level[target.to]) {
                int d = dfs(target.to, goal, min(val, target.cap));
                if (d > 0) {
                    target.cap -= d;
                    Graph[target.to][target.rev].cap += d;
                    return d;
                }
            }
        }
        return 0;
    }
    int run(int s, int t) {
        int ans = 0;
        int f = 0;
        while (bfs(s), level[t] >= 0) {
            itr = vector<int>(Graph.size(), 0);
            while ((f = dfs(s, t, 1e9)) > 0) {
                ans += f;
            }
        }
        return ans;
    }
};

//by ei1333
//https://ei1333.github.io/luzhiled/snippets/structure/segment-tree.html
template< typename Monoid >
struct SegmentTree {
    using F = function< Monoid(Monoid, Monoid) >;

    int sz;
    vector< Monoid > seg;

    const F f;
    const Monoid M1;

    SegmentTree(int n, const F f, const Monoid& M1) : f(f), M1(M1) {
        sz = 1;
        while (sz < n) sz <<= 1;
        seg.assign(2 * sz + 1, M1);
    }

    void set(int k, const Monoid& x) {
        seg[k + sz] = x;
    }

    void build() {
        for (int k = sz - 1; k > 0; k--) {
            seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
        }
    }

    void update(int k, const Monoid& x) {
        k += sz;
        seg[k] = x;
        while (k >>= 1) {
            seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
        }
    }

    Monoid query(int a, int b) {
        Monoid L = M1, R = M1;
        for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
            if (a & 1) L = f(L, seg[a++]);
            if (b & 1) R = f(seg[--b], R);
        }
        return f(L, R);
    }

    Monoid operator[](const int& k) const {
        return seg[k + sz];
    }

    template< typename C >
    int find_subtree(int a, const C& check, Monoid& M, bool type) {
        while (a < sz) {
            Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
            if (check(nxt)) a = 2 * a + type;
            else M = nxt, a = 2 * a + 1 - type;
        }
        return a - sz;
    }


    template< typename C >
    int find_first(int a, const C& check) {
        Monoid L = M1;
        if (a <= 0) {
            if (check(f(L, seg[1]))) return find_subtree(1, check, L, false);
            return -1;
        }
        int b = sz;
        for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
            if (a & 1) {
                Monoid nxt = f(L, seg[a]);
                if (check(nxt)) return find_subtree(a, check, L, false);
                L = nxt;
                ++a;
            }
        }
        return -1;
    }

    template< typename C >
    int find_last(int b, const C& check) {
        Monoid R = M1;
        if (b >= sz) {
            if (check(f(seg[1], R))) return find_subtree(1, check, R, true);
            return -1;
        }
        int a = sz;
        for (b += sz; a < b; a >>= 1, b >>= 1) {
            if (b & 1) {
                Monoid nxt = f(seg[--b], R);
                if (check(nxt)) return find_subtree(b, check, R, true);
                R = nxt;
            }
        }
        return -1;
    }
};

unsigned long xor128() {
    static unsigned long x = 123456789, y = 362436069, z = 521288629, w = 88675123;
    unsigned long t = (x ^ (x << 11));
    x = y; y = z; z = w;
    return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
}

void init() {
    iostream::sync_with_stdio(false);
    cout << fixed << setprecision(20);
}
#define int long long
int calc(State &a) {
    int left = 0;
    while(*a == '-') {
        left++;
        a++;
    }
    if (*a == '(') {
        a++;
        left += calc(a);
        a++;
    }
    else {
        left += *a - '0';
        a++;
    }
    left %= 2;
    int trigger = 0;
    if (*a == '*') {
        trigger = 1;
    }
    a++;
    int right = 0;
    while(*a == '-') {
        right++;
        a++;
    }
    if (*a == '(') {
        a++;
        right += calc(a);
        a++;
    }
    else {
        right += *a - '0';
        a++;
    }
    right %= 2;
    if (trigger == 1) {
        return (left & right);
    }
    else {
        return (left ^ right);
    }
}
int check(string s) {
    s = "0^" + s + ")";
    int ans = 0;
    REP(i, 16) {
        int cnt[4] = {};
        REP(q, 4) {
            if ((1 << q) & i) {
                cnt[q] = 1;
            }
        }
        string c;
        REP(q, s.length()) {
            if (s[q] >= 'a' && s[q] <= 'd') {
                c.push_back(cnt[s[q] - 'a'] + '0');
            }
            else {
                c.push_back(s[q]);
            }
        }
        State now = c.begin();
        ans += (1 << i) * (calc(now));
    }
    return ans;
}
map<int, int> gogo;
void solve() {
    vector<string> expr[20];
    expr[1].push_back("1");
    expr[1].push_back("0");
    expr[1].push_back("a");
    expr[1].push_back("b");
    expr[1].push_back("c");
    expr[1].push_back("d");
    set<int> nekos[20];
    for (int q = 2; q <= 16; ++q) {
        for (auto x : expr[q - 1]) {
            if (x[0] == '-') continue;
            expr[q].push_back("-" + x);
        }
        for (int j = 1; j < q - 3; ++j) {
            int right = (q - 3) - j;
            for (auto x : expr[j]) {
                for (auto y : expr[right]) {
                    if (nekos[q].count(check("(" + x + "*" + y + ")")) == 0) {
                        nekos[q].insert(check("(" + x + "*" + y + ")"));
                        expr[q].push_back("(" + x + "*" + y + ")");
                    }
                    if (nekos[q].count(check("(" + x + "^" + y + ")")) == 0) {
                        nekos[q].insert(check("(" + x + "^" + y + ")"));
                        expr[q].push_back("(" + x + "^" + y + ")");
                    }
                }
            }
        }
    }
    for (int q = 1; q <= 16; ++q) {
        for (auto x : expr[q]) {
            int hoge = check(x);
            gogo[hoge] = max(gogo[hoge], 17 - q);
        }
    }
    while (true) {
        string s;
        cin >> s;
        if (s == ".") return;
        int should_be = check(s);
        cout << 17 - gogo[should_be] << endl;
    }
}

#undef int
int main() {
    init();
    solve();
}